Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Your answer is t=

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or [tex]\frac{2}{1}[/tex]

Perpendicular line's slope = [tex]-\frac{1}{2}[/tex]   (flip the sign from + to -, and flip the fraction)

Slope = [tex]-\frac{3}{4}[/tex]

Perpendicular line's slope = [tex]\frac{4}{3}[/tex]  (flip the sign from - to +, and flip the fraction)

y = 1/3x + 4        The slope is 1/3, so the perpendicular line's slope is [tex]-\frac{3}{1}[/tex] or -3.

Now that you know the slope, substitute/plug it into the equation:

y = mx + b

y = -3x + b       To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself

2= -3(1) + b     Add 3 on both sides to get "b" by itself

2 + 3 = -3 + 3 + b

5 = b

y = -3x + 5

The equation of the line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4) is (y = -3x + 5) and this can be determined by using the given data.

Given :

The line that passes through (1,2) and is perpendicular to the line (y = 1/3x + 4).

The following steps can be used in order to determine the equation of the line:

Step 1 - When two lines are perpendicular to each other then their slopes are:

mm' = 1

where m and m' are the slopes of the lines.

Step 2 - So, the slope of the line which is perpendicular to the line (y = 1/3x + 4) is:

[tex]\rm \dfrac{1}{3}\times m' = -1[/tex]

m' = -3

Step 3 - Now, the equation of a line that passes through the point (1,2) and has a slope -3 is:

[tex]\rm (y -2) = -3(x-1)[/tex]

Step 4 - Simplify the above equation.

y = -3x + 5

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Answer:

a parabola is a curve often resembling a U and follows a mathematical equation

Step-by-step explanation:

for example:

Answer:

In mathematics, a parabola is a plane curve

Step-by-step explanation:

Answer: m = 7 and b = 0

Step-by-step explanation:

y = mx + b is slope-intercept form

m = slope

b = y-intercept

You would put +0 on the end of the equation because it doesn't change anything

The slope of a mountain road with a 10-foot rise for a 494-foot run is found by dividing the rise by the run, resulting in a slope of approximately 0.0202 or 1/49.4, which is a dimensionless ratio.

The student's question involves finding the slope of a mountain road, which is a concept in mathematics. Slope is calculated as 'rise over run', where the 'rise' refers to the change in height and the 'run' refers to the horizontal distance covered. In this instance, the rise is 10 feet and the run is 494 feet.

To calculate the slope of the mountain road, you divide the rise by the run:

Slope = Rise ÷ Run

We substitute the given values:

Slope = 10 ft ÷ 494 ft

The slope is therefore equal to approximately 0.0202 or 1/49.4. In mathematics, slope is dimensionless; it is just the ratio of the rise to the run and does not carry any units.

Answer:

80°

Step-by-step explanation:

Just multiply 40° by 2 to get the arc

Answer:

80

Step-by-step explanation:

An arc's measurement is always twice the amount of its angle.

40 x 2 = 80

Answer:

B-$ 16.89

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

You question is missing some necessary information.

However these are the mappings for the following transformation.

Rotate 180° counterclockwise about the origin. The mapping is

[tex](x,y)\to(-x,-y)[/tex]

Reflect across the line y=x.

The mapping is

[tex](x,y)\to(y,x)[/tex]

Reflect across the line y=-x

The mapping is:

[tex](x,y)\to(-y,-x)[/tex]

Rotate 270° counterclockwise about the origin. The mapping is

[tex](x,y)\to(-y,x)[/tex]

Hope this is helpful.

Please try post complete questions to get the exact answer you are looking for .

Answer:

reflect across the line y = –x (C)

Step-by-step explanation:

If you multiply the point 1,4 by the matrix you get -4, -1

it cant be 180 since that would make it -1,-4 not -4,-1.

y=x would mean its positive making it 4,1

y=-x would mean atleast -x is present and if you use other values it swaps x and y

270 would be x,-y

Answer:

4.5 ft³

Step-by-step explanation:

Volume = base area × height

For base area, find one angle using cosine law

18 inch = 18/12 = 1.5ft

1.5² = 2.5² + 2² - 2(2)(2.5)cos(theta)

cos(theta) = 0.8

sin(theta) = sqrt(1 - 0.8²)

sin(theta) = 0.6

Base area:

½ × 2 × 2.5 × 0.6

1.5

Volume = 1.5 × 3

= 4.5 ft³

Answer:

Step-by-step explanation:

18 inches = 18 × (1/2) ft

                = 1.5 ft

since, this is a right triangle according to the given figure then:

the area of the base (triangle) = 2 × 1.5 = 3 ft²

therefore

the volume = 1.5 × 3

                   = 4.5 ft³

Answer:

14400 cubic inches.

Step-by-step explanation:

Let l, b and h are length, breadth and height of a cuboid respectively, then

[tex]V=l\times b\times h[/tex]

If another cuboid is larger by a scale factor of k, then kl, kb and kh are length, breadth and height of new cuboid respectively.

[tex]V_1=kl\times kb\times kh[/tex]

[tex]V_1=k^3(l\times b\times h)[/tex]

[tex]V_1=k^3V[/tex]       ...(i)

It is given that a kitchen sink has a volume of 1800 cubic inches and a similar sink is larger by a scale factor of 2.

Substitute k=2 and V=1800 in equation (i).

[tex]V_1=2^3(1800)[/tex]

[tex]V_1=14400[/tex]

Therefore, the volume of required sink is 14400 cubic inches.

Answer:

The volume is 14,000

Step-by-step explanation:

v= 2 to the power of 3 times 1800

so 8 x 1800=14,400

Hope this helps!!

Answer:

20

Step-by-step explanation:

You're trying to find the hypotenuse. To do that you have to square 16 and 12. That gets you 256 and 144. You then have to add the 2 numbers. That gets you 400. Finally square root 400 to get 20.

Answer:

B.

Step-by-step explanation:

Sorry I am late. Here's the answer for everybody else. :)

To convert 2 and 5/6 to a percent, convert the fraction to a decimal and add it to the whole number. Then multiply by 100 to find the percentage (approximately 283.3%).

In mathematics, to convert a mixed number like 25/6 to a percentage, you can first convert it to a decimal and then multiply by 100. The fraction can be converted into decimal by dividing the numerator by the denominator. In this case, 5 divided by 6 is approximately 0.8333. Since we have 2 whole and 0.8333, we can add them to get approximately 2.8333. By multiplying this by 100, we get 283.33% which we can take as an approximate value of 283.3% because it's the closest listed option in the question.

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The radius of the oblique cone is; B: 3 units

Formula for the volume of an oblique cone is;

V = ¹/₃πr²h

where;

V is volume

r is radius

h is height

We are told that diameter is equal to the height. Thus;

diameter = 2r = h

Thus;

V = ¹/₃πr²(2r)

18π = ¹/₃πr²(2r)

r = ∛(18π * 3/2π)

r = 3 units

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The radius of the cone is approximately 3 units.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

We have,

We know that the height of the cone is equal to the diameter of the base, which means h = 2r.

Substituting this into the formula for the volume, we get:

V = (1/3) x π x r² x (2r) = (2/3) x π x r³

We are given that the volume of the cone is 187 cubic units, so we can set up an equation:

(2/3) x π x r³  = 187

Multiplying both sides by 3/2π, we get:

r³ = (187 x 3)/(2π)

Taking the cube root of both sides, we get:

r = (187 x 3/(2π))^(1/3) ≈ 3.00

Therefore,

The radius of the cone is approximately 3 units.

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Answer:

7root2/2

Step-by-step explanation:

You can solve this by multiplying by a version of 1 which will simplify but not change the expression. If you multiply this by root2/root2, you will have 7root2 in the numerator and 2 in the denominator, which is simplified. Hope this helps!

Step-by-step explanation:

Use Desmos

Answer:

The rate is [tex]\frac{2}{5}[/tex] degree per hour.

Step-by-step explanation:

Given : A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose [tex]\frac{1}{10}[/tex] degree every [tex]\frac{1}{4}[/tex] hour for a limited time.

To find : What was the rate, in degrees per hour that the temperature of the compound rose ?

Solution :

In every [tex]\frac{1}{4}[/tex] hour the temperature of a compound rose [tex]\frac{1}{10}[/tex] degree

To get  the rate, in degrees per hour,

In every 1 hour the temperature of a compound rose is

[tex]r=\dfrac{\frac{1}{10}}{\frac{1}{4}}[/tex] degree

[tex]r=\dfrac{4}{10}[/tex] degree/hr

[tex]r=\dfrac{2}{5}[/tex] degree/hr

Therefore, the rate is [tex]\frac{2}{5}[/tex] degree per hour.

Answer:

The recipe makes 1/2 cup of salad dressing assuming that the salt and herbs do not make a difference.  Each serving has 1/12 of a cup.  I am not gifted in the number sentence and equation department

Step-by-step explanation:

1/3=2/6

         +

1/6=1/6

--------------

3/6=1/2

The recipe will make 1/2 cup of salad dressing. Each serving would have 1/12 cup of dressing.

To find out how many cups of salad dressing the recipe will make, we can add the quantities of olive oil and balsamic vinegar. We have 1/3 cup of olive oil and 1/6 cup of balsamic vinegar, so the total is 1/3 + 1/6 = 1/2 cup. Therefore, the recipe will make 1/2 cup of salad dressing.

To determine how much dressing there would be in one serving, we divide the total quantity of dressing (1/2 cup) by the number of servings (6). This can be represented as the number sentence: 1/2 ÷ 6 = 1/12 cup per serving.

A term in a math expression is single number or variable and are separated by a + or - or × or ÷

This expression has 4 terms

2r

1c

.5d

and 8

This expression has 4 terms 2r, 1c, 0.5d, and 8.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or the number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given an expression 2r+c+0.5d+8 to find the term of the given expression

A term in a math expression is a single number or variable and is separated by a + or - or × or ÷

thus this equation has four terms

that is:

2r

1c

0.5d

and 8

therefore, Given expression 2r+c+0.5d+8 has 4 terms 2r, 1c, 0.5d, and 8.

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Answer:

36250

1450/ 1/25= 36250

72500

1450/ 1/50

Answer:

6

Step-by-step explanation:

IQR is the distance between the ends of the box. The ends of the box are 15 and 21, so the IQR is 21-15, which is 6.

Answer:

  0.35 ft

Step-by-step explanation:

We assume that the lawnmower is mowing a spiral around the pole and that each turn increases the radius by 2.2 feet. That is, each turn around the pole captures (or releases) 2.2 feet of rope, so that is the circumference of the pole.

  C = 2πr

  2.2 ft = 2(22/7) r

  (2.2 ft)(7/44) = r = 0.35 ft

The radius of the pole needs to be about 0.35 feet, or 4.2 inches.

_____

We assume that the lawnmower width is a multiple of 22 because we are intended to use 22/7 as our approximation of pi. A more accurate value of pi would give a radius of 0.35014 feet, about 4.202 inches.

Answer:

The answer is 43 degrees (plz mark branliest)

Step-by-step explanation:

All triangles must add up to 180 degrees

We have two other angles that are 92 and 45 degrees

If we subtract both of these measurements from 180 we will find x

92 + 45 = 137

180 - 137 = 43 degrees

Hope This Helps!

The length of line segment LN is 6 units.

To determine the length of line segment LN, we can use the segment addition postulate, which states that if you have three collinear points A, B, and C, and point B is between A and C, then AB + BC = AC.

In this case, point M is between L and N. We're given that MN = 2 and LM = 4. So, we can set up the equation:

LM + MN = LN

Substitute the given values:

4 + 2 = LN

Now, calculate the sum:

6 = LN

So, the length of line segment LN is 6 units.

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when the cups of flour increase from 5 to 15, the cups of sugar also increase from 10 to 30, maintaining the constant ratio of 1 : 2.

To find the number of cups of sugar needed when 15 cups of flour are used, let's first determine the constant ratio between cups of flour and cups of sugar.

Given:

- 5 cups of flour are mixed with 10 cups of sugar.

We can set up a ratio:

[tex]\[ \text{Cups of flour} : \text{Cups of sugar} = 5 : 10 \][/tex]

Now, let's simplify this ratio by dividing both parts by their greatest common divisor, which is 5:

[tex]\[ \frac{5}{5} : \frac{10}{5} = 1 : 2 \][/tex]

So, the constant ratio between cups of flour and cups of sugar is 1 : 2.

Now, to find out how many cups of sugar should be used if 15 cups of flour are used, we can use the constant ratio.

[tex]\[ \text{Cups of flour} : \text{Cups of sugar} = 15 : x \][/tex]

Since the ratio is constant, we can use the ratio 1 : 2 to set up a proportion:

[tex]\[ \frac{15}{1} = \frac{x}{2} \][/tex]

Now, let's solve for (x):

[tex]\[ 15 \times 2 = x \times 1 \]\[ 30 = x \][/tex]

So, if 15 cups of flour are used, we will need 30 cups of sugar.

We can also verify this using the constant ratio table:

Cups of flour  Cups of sugar

5                       10

15                      30

As we can see, when the cups of flour increase from 5 to 15, the cups of sugar also increase from 10 to 30, maintaining the constant ratio of 1 : 2.

The probable question maybe:

For a given recipe, 5 cups of flour are mixed with 10 cups of sugar. How many cups of sugar should be used if 15 cups of flour are used? Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x.

Answer:

Step-by-step explanation:11580

Answer:

11580 notebooks

Step-by-step explanation:

3860/4=965 notebooks per day

965x12=11580 notebooks in 12 days

Answer:

57.1 milometer square

Step-by-step explanation:

The surface area is the area that describes the material that will be used to cover a geometric solid. When we determine the surface areas of a geometric solid we take the sum of the area for each geometric form within the solid.

The volume is a measure of how much a figure can hold and is measured in cubic units. The volume tells us something about the capacity of a figure.

A prism is a solid figure that has two parallel congruent sides that are called bases that are connected by the lateral faces that are parallelograms. There are both rectangular and triangular prisms.

Answer : (a+b+c)h=

(4+4+5.7)3=41.1

Answer is 41.1

Answer:

The exterior angle, D, is supplementary to the adjacent interior angle, C. Together, they form a straight line, measuring 180°. The measure of the remote interior angles, A and B are equal to the measure of the exterior angle D.

Step-by-step explanation: I just did the assignment

To solve such problems we need to know about supplementary angles.

When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.

for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.

The exterior angle to ∠C is ∠D, which is the supplementary angle to ∠c and also, to the sum of ∠A and ∠B.

Given information:

A triangle has angles A, B, C. The exterior angle to angle C is angle D.

We know,

Supplementary angles are those two angles whose sum measures up to 180°.

These angles are when adjacent to each other, they form a straight line.

∠C and ∠D form a line BE.

therefore, the ∠C and ∠D are supplementary angles for each other, and

∠C + ∠D = 180°.

∠C = 180° - ∠D

Also, we know that the sum of all angles of a triangle is 180°.

So, ∠A + ∠B + ∠C = 180°

Substituting the value of ∠C,

∠A + ∠B + (180° - ∠D) = 180°

Canceling 180° from both sides,

∠A + ∠B + 180° - ∠D = 180°

∠A + ∠B - ∠D = 0

∠A + ∠B = ∠D

Hence, the exterior angle to ∠C is ∠D, which is the supplementary angle to ∠c and also, to the sum of ∠A and ∠B.

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Answer:

Proportional

Step-by-step explanation:

If she burns 15 per minute, the she will burn 30 in 2 min and 45 in 3 min, etc. Therefore it is proportional.

Answer:

opposite side = 8.27cm

adjacent = 12.5cm

Step-by-step explanation:

to work out the other side of the triangle

give the angle = 32

using SOH CAH TOA

sineФ = opposite/ hypoteneus

sin32° = opposite/ 15cm

using cross multiplication

opposite side = sine32 x 15cm

opposite side = 0.551 x 15cm

opposite side = 8.27cm

to find the other side of the triangle using pythagoras theorem

hypotheneus ² = opposite² + adjacent²

15² = 8.27² + adjacent ²

collect the like terms

15² - 8.27² = adjacent ²

225  - 68.42 = adjacent²

156.58 = adjacent²

squaring both sides

adjacent = √ 156.58

adjacent = 12.5cm

Answer:

Common Ratio = 2

Step-by-step explanation:

Emily started with 12 lb at start.

She will double each day

So,

2nd day she will take up weight = 12 * 2 = 24

3rd day she will take up weight = 24 * 2 = 48

and so on

This is a geometric sequence, which is a sequence where each term is found by multiplying the previous term by a constant which is known as the common ratio.

Here, we are multiplying by "2" to get the next term, so we an say the common ratio is "2".

Answer: Common Ratio = 2

Let's make a table of differences

0 3 8 15 24

3  5 7  9

 2  2  2

Constant second difference means a quadratic polynomial,

f(n)=an² + bn +c

f(1)=0, f(2)=3, f(3)=8

0 = a+b+c

3 = 4a + 2b + c

8 = 9a + 3b + c

Subtracting pairs

3 = 3a+b

5 = 5a + b

Subtracting,

2 = 2a

a = 1

b = 5 - 5a = 0

c = -a-b = -1

f(n)=n² -1

Duh, shoulda noticed that at the beginning.

f(17)=17²-1 = 288

a₁ =5

aₙ = aₙ₋₁ - 7

aₙ = a₁ + d(n-1)

aₙ = 5 - 7(n-1)

a₇ = 5 - 7(6) = -37

Answer: -37